{"id":218,"date":"2023-07-11T08:35:49","date_gmt":"2023-07-11T08:35:49","guid":{"rendered":"https:\/\/mathority.org\/id\/cara-normalisasi-normalisasi-vektor-vektor\/"},"modified":"2023-07-11T08:35:49","modified_gmt":"2023-07-11T08:35:49","slug":"cara-normalisasi-normalisasi-vektor-vektor","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/cara-normalisasi-normalisasi-vektor-vektor\/","title":{"rendered":"Cara menormalkan vektor"},"content":{"rendered":"<p>Di halaman ini Anda akan menemukan pengertian vektor yang dinormalisasi dan bagaimana suatu vektor dinormalisasi dengan beberapa contoh, baik dalam 2 maupun 3 dimensi. Dan, sebagai tambahan, Anda akan menemukan utilitas untuk normalisasi vektor. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-significa-normalizar-un-vector\"><\/span> Apa yang dimaksud dengan normalisasi vektor?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Menormalkan suatu vektor berarti mengubahnya menjadi vektor yang arahnya sama dan arahnya sama tetapi modulnya sama dengan 1. Dengan kata lain, proses normalisasi suatu vektor melibatkan perubahan panjangnya dengan tetap mempertahankan arah dan arahnya. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/normaliser-un-vecteur.webp\" alt=\"\" class=\"wp-image-1096\" width=\"462\" height=\"130\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Jadi, vektor yang dinormalisasi terutama digunakan untuk menunjukkan arah dan makna.<\/p>\n<p> Di sisi lain, ketika Anda menormalkan sebuah vektor, Anda juga menghitung <strong>vektor satuan<\/strong> pada saat yang sama, karena vektor satuan adalah vektor apa pun yang besarnya 1. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-para-normalizar-un-vector\"><\/span> Rumus untuk menormalkan suatu vektor <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> Untuk <strong>menormalkan suatu vektor,<\/strong> setiap komponen vektor harus dibagi dengan modulnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-672f43e570edb18e58ec3fd4fed16aa4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = \\cfrac{\\vv{\\text{v}}}{\\lvert \\vv{\\text{v}}\\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"55\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Emas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah vektor yang dinormalisasi dari <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fe319cb0fecedf2052e6c1e4c856733_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-normalizar-un-vector-en-r2\"><\/span> Contoh normalisasi vektor di R2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sebagai contoh, kita akan menormalkan vektor dua dimensi berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f454b949695fc06cf426821d08d44bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (4,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Pertama-tama kita perlu menghitung modulus (atau amplitudo) vektor. Jika Anda tidak ingat cara melakukannya, Anda dapat melihat <a href=\"https:\/\/mathority.org\/id\/modul-contoh-rumus-vektor-latihan-yang-diselesaikan\/\">rumus besaran vektor<\/a> di sini. Jadi kami menggunakan rumus ini:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f7e5c18e3d72dcd9c628d5326e327c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert  \\vv{\\text{v}} \\rvert = \\sqrt{4^2+3^2} = \\sqrt{25} = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dan kemudian kita membagi vektor dengan modulnya untuk mendapatkan vektor yang dinormalisasi:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5d5c0d56d91c40860fef6064998b03a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{\\text{u}} = \\cfrac{\\vv{\\text{v}}}{\\lvert \\vv{\\text{v}}\\rvert} = \\cfrac{(4,3)}{5} = \\left( \\frac{4}{5} , \\frac{3}{5} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"200\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Biasanya ketika sebuah vektor dinormalisasi, ia tetap berupa pecahan, namun Anda dapat meneruskannya ke desimal tanpa masalah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-normalizar-un-vector-en-r3\"><\/span> Contoh normalisasi vektor di R3 <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p> Agar Anda dapat melihat contoh lainnya, kami akan menormalkan vektor tiga dimensi berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-248a85e7c4c82cd4b585788acc7a8e16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (2,-1,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Pertama, kita menghitung besar vektornya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-65c38c65791e6029f6af679d3e9a7b6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert  \\vv{\\text{v}} \\rvert = \\sqrt{2^2+(-1)^2+4^2} = \\sqrt{21}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"236\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> Dan terakhir, kita membagi vektor dengan modulnya untuk menormalkannya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9db02c90bc7fc8aba5e93aae28665263_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{\\text{u}} = \\cfrac{\\vv{\\text{v}}}{\\lvert \\vv{\\text{v}}\\rvert} = \\cfrac{(2,-1,4)}{\\sqrt{21}} = \\left( \\frac{2}{\\sqrt{21}} , \\frac{-1}{\\sqrt{21}} , \\frac{4}{\\sqrt{21}}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"322\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfpara-que-sirve-normalizar-un-vector\"><\/span> Apa gunanya normalisasi vektor?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Melihat penerapan normalisasi vektor tidaklah mudah, bahkan mungkin terlihat bahwa vektor yang dinormalisasi lebih buruk daripada vektor \u201cnormal\u201d, karena sering kali memiliki pecahan dan lebih sulit untuk menangani pecahan.<\/p>\n<p> Namun, beberapa operasi vektor menjadi lebih sederhana jika menggunakan vektor yang dinormalisasi. Misalnya, mencari sudut antara dua vektor akan lebih mudah jika keduanya memiliki modulus (atau besaran) sama dengan satu. Selain itu, sudut yang dibentuk oleh dua vektor tidak bergantung pada panjangnya tetapi pada arahnya, sehingga sangat mungkin untuk menormalkan terlebih dahulu kedua vektor tersebut dan kemudian mencari sudut yang dibentuknya.<\/p>\n<p> Jika Anda lebih tertarik pada cara menghitung sudut antara dua vektor dan mengapa lebih mudah melakukannya dengan vektor yang dinormalisasi, Anda dapat melihat halaman <a href=\"https:\/\/mathority.org\/id\/cara-menghitung-sudut-antara-dua-vektor-contoh-latihan-yang-diselesaikan\/\">sudut antara dua vektor<\/a> . Di sini Anda akan menemukan semua penjelasan, serta contoh dan latihan yang diselesaikan.<\/p>\n<p> Karakteristik vektor yang dinormalisasi ini sangat berguna pada tingkat komputasi. Karena waktu yang Anda hemat untuk melakukan satu operasi vektor sangat rendah. Namun jika puluhan ribu operasi harus dilakukan, seperti halnya dengan komputer, penghematan waktu cukup besar.<\/p>\n<p> Terakhir, basis vektor yang umum digunakan adalah basis ortonormal, karena dengan basis tersebut lebih mudah untuk menyatakan koordinat suatu vektor dan, sebagai tambahan, memudahkan banyak perhitungan dengan matriks dalam aljabar linier. Nah, semua vektor dari jenis basis ini adalah vektor yang dinormalisasi. Misalnya, <a href=\"https:\/\/mathority.org\/id\/sistem-koordinat-bola-silinder-kutub-kartesius\/\">sistem koordinat<\/a> Kartesius merupakan basis ortonormal.<\/p>\n<p> Kesimpulannya, vektor yang dinormalisasi tidak sepenuhnya diperlukan karena semua operasi antar vektor dapat dilakukan tanpa vektor tersebut, namun hal ini sangat memudahkan perhitungan.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan menemukan pengertian vektor yang dinormalisasi dan bagaimana suatu vektor dinormalisasi dengan beberapa contoh, baik dalam 2 maupun 3 dimensi. Dan, sebagai tambahan, Anda akan menemukan utilitas untuk normalisasi vektor. Apa yang dimaksud dengan normalisasi vektor? Menormalkan suatu vektor berarti mengubahnya menjadi vektor yang arahnya sama dan arahnya sama tetapi modulnya &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/cara-normalisasi-normalisasi-vektor-vektor\/\"> <span class=\"screen-reader-text\">Cara menormalkan vektor<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[54],"tags":[],"class_list":["post-218","post","type-post","status-publish","format-standard","hentry","category-vektor"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Cara normalisasi vektor - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/cara-normalisasi-normalisasi-vektor-vektor\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cara normalisasi vektor - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan menemukan pengertian vektor yang dinormalisasi dan bagaimana suatu vektor dinormalisasi dengan beberapa contoh, baik dalam 2 maupun 3 dimensi. 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Dan, sebagai tambahan, Anda akan menemukan utilitas untuk normalisasi vektor. Apa yang dimaksud dengan normalisasi vektor? 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